Question

If the lateral surface area of a cylinder is the circumference of base x height of a cylinder, can we write the lateral surface area of a cuboid as perimetre of base x height of a cuboid?

Answer 1

Dear student

$$\begin{gathered} Lateralsurfaceareaofcylinder=2\mathrm{\pi rh},\mathrm{where}\mathrm{r}\mathrm{is}\mathrm{the}\mathrm{radius}\mathrm{and}\mathrm{h}\mathrm{is}\mathrm{the}\mathrm{height}. \\ \mathrm{A}.\mathrm{T}.\mathrm{Q} \\ \mathrm{Lateral}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{cylinder}=\mathrm{circumference}\mathrm{of}\mathrm{base}\times \mathrm{height}\mathrm{of}\mathrm{cylinder} \\ \Rightarrow 2\mathrm{\pi rh}=2\mathrm{\pi r}\times \mathrm{h} \\ \mathrm{Lateral}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{cuboid}=2\left(\mathrm{l}+\mathrm{b}\right)\mathrm{h}\mathrm{where}\mathrm{l}=\mathrm{length},\mathrm{b}=\mathrm{breadth},\mathrm{h}=\mathrm{height} \\ \mathrm{Perimeter}\mathrm{of}\mathrm{base}=2(\mathrm{l}+\mathrm{b}) \\ \mathrm{So},\mathrm{Perimeter}\mathrm{of}\mathrm{base}\times \mathrm{Height}\mathrm{of}\mathrm{cuboid}=2\left(\mathrm{l}+\mathrm{b}\right)\mathrm{h}=\mathrm{Lateral}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{cuboid} \end{gathered}$$
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